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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Jacobian variety; isogeny; theta group; theta function; discrete logarithm problem; non-hyperelliptic curve Isogeny, Jacobians, Prym varieties, Theta functions and abelian varieties, Cryptography, Algebraic moduli of abelian varieties, classification, Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry, Authentication, digital signatures and secret sharing, Algebraic coding theory; cryptography (number-theoretic aspects) Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with \((\ell ,\ell ,\ell)\)-isogenies
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Shimura G, On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields,Nagoya Math. J. 43 (1971) 199--208 Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry, Elliptic curves, Elliptic curves over global fields, Abelian varieties of dimension \(> 1\), Complex multiplication and moduli of abelian varieties, Homogeneous spaces and generalizations, Complex multiplication and abelian varieties, Jacobians, Prym varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) N. Bruin, E.V. Flynn,Towers of 2-covers of hyperelliptic curves, Trans. Amer. Math. Soc. 357 (2005), 4329-4347. Zbl1145.11317 MR2156713 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties Towers of 2-covers of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic theory H. Popp, ?Über das Verhalten des Geschlecht eines Funktionenkörpers einer Variablen bei Konstantenreduktion,? Math. Z.,106, No. 1, 17?35 (1968). Algebraic functions and function fields in algebraic geometry Über das Verhalten des Geschlechts eines Funktionenkörpers einer Variablen bei Konstantenreduktion
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Witt ring of a ring; real algebraic curve; Knebusch-Milnor sequence Algebraic theory of quadratic forms; Witt groups and rings, Witt groups of rings, Forms over real fields, Algebraic functions and function fields in algebraic geometry Splitting natural injection of Witt rings of geometric rings
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell conjecture for function fields; theorem of the kernel doi:10.2307/2374831 Rational points, Arithmetic theory of algebraic function fields, History of algebraic geometry A note on Manin's theorem of the kernel
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic over function fields; height theory; Lang and Vojta conjectures Arithmetic varieties and schemes; Arakelov theory; heights, Rigid analytic geometry, Heights, Algebraic functions and function fields in algebraic geometry On some differences between number fields and function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane quartics; rational points; local-to-global obstructions; bitangents; descent obstructions; two-covers Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Plane and space curves Two-cover descent on plane quartics with rational bitangents
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Fundamental systems of algebraic functions Algebraic functions and function fields in algebraic geometry On the theory of algebraic functions.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of arbitrary genus; 2-descent on Jacobians; Chabauty-Coleman method; graph of rational preperiodic points of a quadratic polynomial; number of preperiodic points Poonen, B, The classification of rational preperiodic points of quadratic polynomials over \({ Q}\): a refined conjecture, Math. Z., 228, 11-29, (1998) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) modular curves; Atkin-Lehner involution; Heegner points; exceptional rational point Galbraith, SD, Rational points on \(X_0^+(p)\), Exp. Math., 8, 311-318, (1999) Rational points, Elliptic curves over global fields, Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves Rational points on \(X_0^+(p)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) divisor on a \(\widehat Z\)-submodule \(M\) of a curve over a finite field; effective divisor; linear equivalence of a divisor on \(M\) Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry \(\widehat Z\)-submodules of curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) superelliptic Jacobians; homomorphisms of abelian varieties Zarhin Yu.G. (2006). Non-isogenous superelliptic jacobians. Math. Z. 253: 537--554 Jacobians, Prym varieties, Isogeny, Curves of arbitrary genus or genus \(\ne 1\) over global fields Non-isogenous superelliptic Jacobians
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weierstrass semigroup; asymptotically good tower of function fields Pellikaan R., Stichtenoth H., Torres F. (1998). Weierstrass semigroups in an asymptotically good tower of function fields. Finite Fields Appl 4(4):381--392 Arithmetic theory of algebraic function fields, Curves over finite and local fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic ground fields for curves, Riemann surfaces; Weierstrass points; gap sequences Weierstrass semigroups in an asymptotically good tower of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Diophantine quintuples; rational points; elliptic curves Quadratic and bilinear Diophantine equations, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Jacobians, Prym varieties, Computer solution of Diophantine equations, Global ground fields in algebraic geometry, Other nonalgebraically closed ground fields in algebraic geometry, Arithmetic ground fields for curves, Elliptic curves Diagonal genus 5 curves, elliptic curves over \(\mathbb{Q}(t)\), and rational Diophantine quintuples
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; algebraic varieties; divisors; line bundles; vector bundles; sheaves; cohomology; elliptic curves; curves over arithmetic fields; Belyi's theorem; algebraic curves; one-dimensional varieties; coherent sheaves on curves; Riemann-Roch theorem; hyperelliptic curves; Serre duality Algebraic functions and function fields in algebraic geometry, Vector bundles on curves and their moduli, Valuations and their generalizations for commutative rings, Elliptic curves, Riemann-Roch theorems, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to commutative algebra, Arithmetic ground fields for curves Algebraic curves and one-dimensional fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points; families of covers of the projective line; moduli problem; Hurwitz monodromy group; Nielsen class; ramification locus; degrees of the rational divisors J.H. Conway and R.A. Parker , On the Hurwitz number of arrays of group elements . Preprint [DFr1] P. Dèbes and M. Fried , Arithmetic variation of fibers , J. für die reine und angew. Math 400 ( 1990 ), 106 - 137 . Zbl 0699.14033 Ramification problems in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Separable extensions, Galois theory, Coverings of curves, fundamental group Arithmetic variation of fibers in families of curves. I: Hurwitz monodromy criteria for rational points on all members of the family
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) central simple algebras; irreducible lattices; rings of invariants; function fields; normal varieties; coordinate rings; reduced traces; Cayley-Hamilton algebras; étale local classes; smooth orders Lieven Le Bruyn, ''Non-smooth algebra with smooth representation variety (asked in MathOverflow)'', Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Finite-dimensional division rings, Algebraic functions and function fields in algebraic geometry, Actions of groups and semigroups; invariant theory (associative rings and algebras) Local structure of Schelter-Procesi smooth orders
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Arithmetische Begründung einiger algebraischer Fundamentalsätze.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; Eichler orders; quotient graphs; vector bundles Vector bundles on curves and their moduli, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Groups acting on trees On genera containing non-split Eichler orders over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Bilinear and Hermitian forms, Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Algebraic functions and function fields in algebraic geometry, Finite-dimensional division rings, Rings with involution; Lie, Jordan and other nonassociative structures Erratum to ``Hermitian \(u\)-invariants over function fields of \(p\)-adic curves''
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Rational triangle; elliptic curve Quadratic and bilinear Diophantine equations, Arithmetic theory of algebraic function fields, Elliptic curves On the area of rational triangles
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cubic polynomials; cubic curves; characteristic property; collinearity; group operation Algebraic functions and function fields in algebraic geometry, Plane and space curves, One-variable calculus The cubic curve is an adding machine
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Zeta and \(L\)-functions in characteristic \(p\), Finite ground fields in algebraic geometry On the number of places of function fields and congruence zeta functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curves; discriminant; Weierstrass equation; good reduction Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Arithmetic ground fields (finite, local, global) and families or fibrations, Arithmetic ground fields for curves Global Weierstrass equations of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic geometry; hyperelliptic curves; bielliptic curves; quadratic points; elliptic curves; modular curves; involutions Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for curves Bielliptic modular curves \(X_0^\ast(N)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; Clifford algebra; Heisenberg algebra; quantum field theories; Ward identities; reciprocity laws L. A. Takhtajan, ``Quantum field theories on an algebraic curve'', Lett. Math. Phys., 52:1 (2000), 79 -- 91 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Algebraic functions and function fields in algebraic geometry, Relationships between algebraic curves and physics Quantum field theories on an algebraic curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) classfield towers; finite field; lower bounds; rational points; algebraic curve Perret, Tours Ramifiées Infinies de Corps de Classes, J. Number Theory 38 pp 300-- (1991) Class field theory, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry Tours ramifiées infinies de corps de classes. (Infinite ramified class field towers)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; rational points; global function field; asymptotic bound Xing, C.; Yeo, S. L., Algebraic curves with many points over the binary field, J. Algebra, 311, 775-780, (2007) Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields Algebraic curves with many points over the binary field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) higher degree diophantine equations; reducibility; Dickson polynomials; Ritt's second theorem; plane curves Bilu, Yuri F.; Tichy, Robert F., The Diophantine equation \(f(x)=g(y)\), Acta Arith., 95, 3, 261-288, (2000) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves The Diophantine equation \(f(x) = g(y)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) 2-Selmer group; hyperelliptic curve; function field; Jacobian Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties Average size of 2-Selmer groups of Jacobians of odd hyperelliptic curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Fermat curve; Jacobian; algebraic point Tzermias P.: Algebraic points of low degree on the Fermat curve of degree seven. Manuscripta Math. 97, 483--488 (1998) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Special algebraic curves and curves of low genus Algebraic points of low degree on the Fermat curve of degree seven
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) (Equivariant) Chow groups and rings; motives, Transcendental methods, Hodge theory (algebro-geometric aspects), Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) section conjecture; hyperbolic curves over function fields; finitely generated fields Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Coverings of curves, fundamental group, Rational points On the section conjecture over function fields and finitely generated fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer group; Galois group; obstruction group; curve of genus 1; principal homogeneous space for an elliptic curve Elliptic curves, Brauer groups of schemes, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Invariants of simple algebras over function fields of principal homogeneous spaces of elliptic curves over number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) P. Corvaja and U. Zannier, On integral points on surfaces, Ann. of Math. (2) 160 (2004), no. 2, 705-726. Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry On integral points on surfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Sato Grassmannian; \(p\)-adic tau function; \(p\)-adic loop group; formal group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic number theory: local fields, Jacobians, Prym varieties Introduction to \(p\)-adic soliton theory
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) coordinate ring of algebraic curve; differential operators Commutative rings of differential operators and their modules, Rings of differential operators (associative algebraic aspects), Algebraic functions and function fields in algebraic geometry Generators of rings of differential operators on a class of \(k\)-algebras
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weierstrass points; maximal curves; Kummer extensions Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields Weierstrass points on Kummer extensions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) primitive roots; Artin's conjecture; function field; Dirichlet density of prime ideals Clark, D. A.; Kuwata, M.: Generalized Artin's conjecture for primitive roots and cyclicity mod p of elliptic curves over function fields. Canad. math. Bull. 38, No. 2, 167-173 (1995) Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Generalized Artin's conjecture for primitive roots and cyclicity mod \({\mathfrak p}\) of elliptic curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Finite simple groups and their classification Applications of curves over finite fields. (Preface).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cyclic function fields; \(L\)-functions unctions of functions fields; mean value of \(L\)-functions; zeta functions; function; class number Rosen, M.: Average value of class numbers in cyclic extensions of the rational function field. In: Number Theory. (Halifax, NS, 1994), pp. 307-323, CMS Conference Proceedings, vol. 15. American Mathematical Society, Providence, RI (1995) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Rate of growth of arithmetic functions, Other algebras and orders, and their zeta and \(L\)-functions, Class groups and Picard groups of orders, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry Average value of class numbers in cyclic extensions of the rational function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tractability; function fields; genus one; quaternion algebra; global field Arithmetic theory of algebraic function fields, Brauer groups (algebraic aspects), Brauer groups of schemes Tractability of algebraic function fields in one variable of genus one over global fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphic form; Drinfeld shtuka; Langlands correspondence; moduli stack of shtukas; global Langlands conjecture; function fields Laumon, G.: Chtoucas de Drinfeld et correspondance de Langlands. Gaz. Math. \textbf{88}, 11-33 (2001) Drinfel'd modules; higher-dimensional motives, etc., Langlands-Weil conjectures, nonabelian class field theory, Arithmetic theory of algebraic function fields, Algebraic moduli problems, moduli of vector bundles Drin'feld shtukas and Langlands correspondence (following Laurent Lafforgue)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arithmetic theory of algebraic functions; Dedekind-Weber theory; algebraic function fields; linear systems; divisors; Abelian differentials Algebraic functions and function fields in algebraic geometry On the theory of algebraic functions of one variable and \textit{Abel}ian integrals
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Periods of algebraic integrals Algebraic functions and function fields in algebraic geometry On residues relative to asymptotes. Classification of the quatratices of algebraic curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) gauge fields; principal bundles; arithmetic schemes; algebraic number fields; Galois groups; class field theory Relationships between algebraic curves and physics, Vector bundles on curves and their moduli, Class field theory, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Arithmetic gauge theory: a brief introduction
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic curves; Algebraic functions of one variable Algebraic functions and function fields in algebraic geometry, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences Algebraic functions considered geometrically (continuation).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quasi-periodic solutions; BKP hierarchy; quasi-periodic \(\tau \) - functions; theta functions; Prym varieties of algebraic curves; wave functions; soliton solutions; Abelian integrals; pole divisor; Riemann's theta function .Publ. RIMS, Kyoto Univ. 18 (1982), 1111--1119; Partial differential equations of mathematical physics and other areas of application, Algebraic functions and function fields in algebraic geometry, Group varieties, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Quasi-periodic solutions of the orthogonal KP equation. Translation groups for soliton equations. V
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) AG codes; algebraic geometric codes; function field tower; Gilbert-Varshamov bound; integral basis Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) Integral bases in a tower of algebraic function fields: a contribution to the construction of asymptotically good algebraic-geometric codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) set of rational points; number of rational points of curves Pacelli, P., Uniform boundedness for rational points, Duke Math. J., 88, 77-102, (1997) Rational points, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Uniform boundedness for rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finiteness of integral points; prime characteristic; abelian variety over a function field Voloch, J.F., Diophantine approximation on abelian varieties in characteristic \textit{p}, Amer. J. math., 117, 4, 1089-1095, (1995) Varieties over global fields, Algebraic theory of abelian varieties, Abelian varieties of dimension \(> 1\), Algebraic functions and function fields in algebraic geometry, Diophantine approximation, transcendental number theory Diophantine approximation on abelian varieties in characteristic \(p\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell conjecture; number of rational points; Vojta's method; Faltings theorem; genus; rank of Mordell-Weil group; Jacobian; points of small height; modular height Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Counting solutions of Diophantine equations A polynomial approach to Faltings's theorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) superelliptic curve; cyclic Galois groups Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Twists of superelliptic curves without rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves; Jacobian varieties Howe, E., Infinite families of pairs of curves over \(\mathbb{Q}\) with isomorphic Jacobians, J. lond. math. soc., 72, 327-350, (2005) Jacobians, Prym varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus Infinite families of pairs of curves over \(\mathbb{Q}\) with isomorphic Jacobians
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Weil rank; elliptic surface; elliptic curve; Tate's conjecture Silverman, J.: A bound for the Mordell-Weil rank of an elliptic curve after a cyclic base extension. J. Alg. Geom. 9, 301--308 (2000) Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves, Rational points, Algebraic functions and function fields in algebraic geometry A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann surface; resolution of singularities; Newton polygon Brieskorn, E., Knörrer, H.: Plane Algebraic Curves. Birkhäuser, Basel (1986) Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, History of algebraic geometry, Singularities of curves, local rings, Compact Riemann surfaces and uniformization, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Implicit function theorems; global Newton methods on manifolds, Projective analytic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Algebraic functions and function fields in algebraic geometry Plane algebraic curves. Transl. from the German by John Stillwell
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hurwitz spaces; meromorphic functions; Severi varieties Ongaro J and Shapiro B 2015 A note on planarity stratification of Hurwitz spaces \textit{Can. Math. Bull.}58 596--609 Plane and space curves, Algebraic functions and function fields in algebraic geometry, Riemann surfaces A note on planarity stratification of Hurwitz spaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) reduction of Riemann theta-functions to lower genera; integrable nonlinear equations; symmetries; finite-zone solutions M. V. Babich, A. I. Bobenko, and V. B. Matveev, Reductions of Riemann theta functions of genus \? to theta functions of lesser genus, and symmetries of algebraic curves, Dokl. Akad. Nauk SSSR 272 (1983), no. 1, 13 -- 17 (Russian). Partial differential equations of mathematical physics and other areas of application, Theta functions and abelian varieties, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Analytic theory of abelian varieties; abelian integrals and differentials, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Reductions of Riemann theta-functions of genus g to theta-functions of lower genus, and symmetries of algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) local complete intersection; algorithm; generator of ideal of curve Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry, Complete intersections Computing the minimal number of equations defining an affine curve ideal-theoretically
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic curves; places; irreducibility Algebraic functions and function fields in algebraic geometry On a direct method to decompose a given rational function of two independent variables into irreducible factors
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) conjecture of Brumer-Stark; global function field; Bruhat-Tits tree; values of partial zeta functions Arithmetic theory of algebraic function fields, Local ground fields in algebraic geometry Rigid analytic methods in the arithmetic theory of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of genus two; elliptic curves; elliptic differential Kani E.(1997). The existence of curves of genus 2 with elliptic differentials. J. Number Theory 64, 130--161 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves The existence of curves of genus two with elliptic differentials
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curve; étale \(K\)-theory; curve; Hasse principle \(K\)-theory of schemes, Galois cohomology, Relations of \(K\)-theory with cohomology theories, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Hasse principle, weak and strong approximation, Brauer-Manin obstruction Note on linear relations in Galois cohomology and étale \(K\)-theory of curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arakelov geometry; arithmetic surface; noncommutative geometry; Archimedean cohomology; Cuntz-Krieger algebra, spectral triple; directed graph; Schottky uniformization; Mumford curve; dynamical cohomology Consani, C.; Marcolli, M.: New perspectives in Arakelov geometry. CRM proc. Lecture notes 36, 81-102 (2004) Noncommutative geometry (à la Connes), Arithmetic varieties and schemes; Arakelov theory; heights, Noncommutative dynamical systems, Curves of arbitrary genus or genus \(\ne 1\) over global fields New perspectives in Arakelov geometry
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Fermat equation; integral solutions Higher degree equations; Fermat's equation, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Coverings of curves, fundamental group Non-abelian descent and the generalized Fermat equation
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) parametric piecewise algebraic curve; singular points; semi-algebraic set; numerical examples; bivariate spline function Computer-aided design (modeling of curves and surfaces), Algebraic functions and function fields in algebraic geometry, Numerical computation using splines The maximum number and its distribution of singular points for parametric piecewise algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic functions and function fields in algebraic geometry On the determination of a fundamental systsem for a given genus domain of algebraic functions of a variable x.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) vector bundle over smooth projective curve Laumon, G, Un analogue global du cône nilpotent, Duke Math. J., 57, 647-671, (1988) Algebraic functions and function fields in algebraic geometry Un analogue global du cône nilpotent. (A global analogue of the nilpotent cone)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Model-theoretic algebra, Classification theory, stability, and related concepts in model theory, Abelian varieties of dimension \(> 1\), Rational points, Algebraic functions and function fields in algebraic geometry On function field Mordell-Lang: the semiabelian case and the socle theorem
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curve; congruence subgroup; eigenvalue; Laplacian Yau, S.-T. An application of eigenvalue estimate to algebraic curves defined by congruence subgroups,Math. Res. Lett. 3(2), 167--172, (1996). Spectral problems; spectral geometry; scattering theory on manifolds, Algebraic functions and function fields in algebraic geometry An application of eigenvalue estimate to algebraic curves defined by congruence subgroups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curve; division algebra; algebraic index; period; Brauer group; period-index problem Skew fields, division rings, Arithmetic theory of algebraic function fields, Algebraic theory of abelian varieties The algebraic index of a division algebra
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) norm group; birational invariant; complete variety; function field Rost, M.: Durch Normengruppen definierte birationale Invarianten. C. R. Acad. Sci. Paris Sér. I, Mathématiques. 310, 189-192 (1990) Rational and birational maps, Algebraic functions and function fields in algebraic geometry Durch Normengruppen definierte birationale Invarianten. (Birational invariants defined by norm groups)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) genus 2 curve; Fricke involution; Jacobian Arithmetic aspects of modular and Shimura varieties, Jacobians, Prym varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Picard schemes, higher Jacobians The modular points of a genus 2 quotient of \(X_0(67)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) pseudoglobal field; algebraic curve; Brauer group; Tate-Shafarevich group Brauer groups of schemes, Algebraic functions and function fields in algebraic geometry, Global ground fields in algebraic geometry On the Brauer groups and the Tate-Shafarevich groups of curves over pseudoglobal fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global field of positive characteristic; Langlands conjecture; \(\ell\)-adic representations; Weil group; automorphic cuspidal representations; adele V. G. Drinfel\(^{\prime}\)d, Two-dimensional \?-adic representations of the Galois group of a global field of characteristic \? and automorphic forms on \?\?(2), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 138 -- 156 (Russian, with English summary). Automorphic functions and number theory, II. Langlands-Weil conjectures, nonabelian class field theory, Representations of Lie and linear algebraic groups over global fields and adèle rings, Representation-theoretic methods; automorphic representations over local and global fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Two-dimensional \(\ell\)-adic representations of the Galois group of a global field of characteristic \(p\) and automorphic forms on \(\mathrm{GL}(2)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points of bounded degree on a curve; Faltings' theorem; Mordell's conjecture; Brill-Noether loci; Jacobian Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields Points of degree \(d\) on curves over number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Group of automorphisms; algebraic function fields; Galois extensions A. Kontogeorgis, The group of automorphisms of cyclic extensions of rational function fields, Journal of Algebra 216 (1999), 665--706. Arithmetic theory of algebraic function fields, Galois theory, Inverse Galois theory, Finite automorphism groups of algebraic, geometric, or combinatorial structures The group of automorphisms of cyclic extensions of rational function fields
| 1 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite groups; automorphism groups of function fields; hyperelliptic function-field R. Brandt, Über die Automorphismengruppen von algebraischen Funktionenkörpern, PhD thesis, Universität Essen, 1988. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the groups of automorphisms of algebraic function fields.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hurwitz bound; \(p\)-ranks; abelian subgroups of \(\Aut(X)\) Nakajima, S.: On automorphism groups of algebraic curves. In: Current Trends in Number Theory, pp. 129--134. Hindustan Book Agency, New Delhi (2002) Automorphisms of curves, Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Jacobians, Prym varieties On automorphism groups of algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) inverse Galois problem; Galois extension of function field; Riemann- Hurwitz formula; genus; mock covers of curves DOI: 10.2307/2159335 Algebraic functions and function fields in algebraic geometry, Inverse Galois theory, Birational automorphisms, Cremona group and generalizations, Automorphisms of curves, Arithmetic theory of algebraic function fields, Curves in algebraic geometry The automorphism group of a function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) congruence function field; automorphism group; Galois group; ramification Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Representations of groups as automorphism groups of algebraic systems Groups of automorphisms of global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms group of the Fermat curve P. Barraza, Curvas de Fermat y descomposición de objetos asociados, Master thesis, Pontificia Universidad Católica de Chile, (2009). Coverings of curves, fundamental group, Birational automorphisms, Cremona group and generalizations The group of automorphisms of the Fermat curve
| 1 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann surfaces; automorphisms Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences, Group actions on affine varieties, Compact Riemann surfaces and uniformization The group of automorphisms of the Fermat curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group of the modular curve ] F. Momose, Automorphism groups of the modular curves \(X_{1}(N)\). Preprint. Arithmetic ground fields for curves, Modular and automorphic functions, Group actions on varieties or schemes (quotients) Automorphism groups of the modular curves \(X_ 0(N)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann-Hurwitz formula; trace characters Kuribayashi, On automorphism groups of a curve as linear groups, J. Math. Soc. Japan 39 pp 51-- (1987) Coverings of curves, fundamental group, Differentials on Riemann surfaces, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Fuchsian groups and their generalizations (group-theoretic aspects) On automorphism groups of a curve as linear groups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; Hurwitz genus formula; nilpotent group; positive characteristic Algebraic functions and function fields in algebraic geometry, Automorphisms of curves On nilpotent automorphism groups of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms; survey; Riemann surfaces; algebraic function fields; Kummer extensions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Automorphisms of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Singh B. On the group of automorphisms of a function field of genus at least two. J Pure Appl Algebra, 4: 205--229 (1975) Arithmetic theory of algebraic function fields, Ramification and extension theory, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry On the group of automorphisms of a function field of genus at least two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Atkin-Lehner involutions; modular curves Arithmetic aspects of modular and Shimura varieties, Holomorphic modular forms of integral weight, Automorphisms of curves, Special algebraic curves and curves of low genus The automorphism group of the modular curve \(X_0^*(N)\) with square-free level
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups; Klein surfaces; N. E. C. groups; real algebraic curve of genus two Special algebraic curves and curves of low genus, Representations of groups as automorphism groups of algebraic systems, Group actions on varieties or schemes (quotients), Other geometric groups, including crystallographic groups, Riemann surfaces Automorphism groups of algebraic curves of \(R^ n\) of genus 2
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field of a curve; geometric Goppa codes; automorphism groups; one-point codes; Xing's theorem Kondo, S.; Katagiri, T.; Ogihara, T., Automorphism groups of one-point codes from the curves \(y^q + y = x^{q^r + 1}\), IEEE trans. inf. theory, 47, 2573-2579, (2001) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic codes Automorphism groups of one-point codes from the curves \(y^q+y=x^{q^r+1}\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hurwitz inequality; coverings of curves; bounds for order of abelian subgroups of automorphism group of algebraic curve; characteristic p S. Nakajima,On abelian automorphism groups of algebraic curves, Journal of the London Mathematical Society (2)36 (1987), 23--32. Special algebraic curves and curves of low genus, Coverings of curves, fundamental group, Group actions on varieties or schemes (quotients) On abelian automorphism groups of algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic curves; automorphism groups Computational aspects of algebraic curves, Automorphisms of curves, Coverings of curves, fundamental group, Software, source code, etc. for problems pertaining to algebraic geometry On calculation of the group of automorphisms of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of rational points; Deligne-Lusztig curves; function fields; large groups of automorphisms; Goppa codes HP Johan~P. Hansen and Jens~Peter Pedersen, \emph Automorphism groups of Ree type, Deligne-Lusztig curves and function fields, J. Reine Angew. Math. \textbf 440 (1993), 99--109. Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic ground fields for curves, Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Automorphism groups of Ree type, Deligne-Lusztig curves and function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational quaternion algebra; Atkin-Lehner group; bielliptic Shimura curves; rational points; elliptic Atkin-Lehner quotients V. Rotger, On the group of automorphisms of Shimura curves and applications, Compositio Mathematica 132 (2002), 229--241. Arithmetic aspects of modular and Shimura varieties, Modular and Shimura varieties On the group of automorphisms of Shimura curves and applications
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; automorphisms; Riemann surfaces; superelliptic curves Automorphisms of curves, Compact Riemann surfaces and uniformization, Families, moduli of curves (algebraic), Special algebraic curves and curves of low genus, Coverings of curves, fundamental group, Research exposition (monographs, survey articles) pertaining to algebraic geometry On automorphisms of algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) modular curve; automorphism group; hyperelliptic curve; hyperelliptic involution Daeyeol Jeon, Automorphism groups of hyperelliptic modular curves, Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 7, 95 -- 100. Automorphisms of curves, Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties Automorphism groups of hyperelliptic modular curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism; curves; positive characteristic; \(p\)-rank; Hurwitz bound Giulietti, M.; Korchmáros, G., Automorphism groups of algebraic curves with \textit{p}-rank zero, J. Lond. Math. Soc., 81, 2, 277-296, (2010) Automorphisms of curves Automorphism groups of algebraic curves with \(p\)-rank zero
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) linear groups; real curves; projective curves; function fields; strong Hasse principle; homogeneous spaces; existence of \(K\)-rational points; weak approximation; density of local points; diagonal image; central isogeny; principal homogeneous spaces; projective algebraic varieties; reciprocity law; obstruction to the Hasse principle; obstruction to weak approximation; Galois cohomology Jean-Louis Colliot-Thélène, Groupes linéaires sur les corps de fonctions de courbes réelles, J. Reine Angew. Math. 474 (1996), 139 -- 167 (French). Galois cohomology of linear algebraic groups, Algebraic functions and function fields in algebraic geometry, Real algebraic and real-analytic geometry, Linear algebraic groups over adèles and other rings and schemes, Homogeneous spaces and generalizations Linear groups on the function fields of real curves
| 0 |
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